MA 15200
Lesson 2
Section P.1 (part 2)
I
More on Evaluating Algebraic Expressions
Reminder: The Order of Operations Agreement
1. Perform operations within the innermost grouping and work outwards. If
the expression involves a fraction, treat the numerator and denominator as if
they were each a group. Grouping can include parentheses, brackets, a root,
or absolute value bars.
2. Evaluate all exponential expressions.
3. Perform multiplication and/or division as they occur, working from left to
right.
4. Perform addition and/or subtraction as they occur, working from left to
right.
Ex 1: Evaluate:
12  2  32
 43  (3)3   1
Ex 2: Evaluate:
32  80  23  3  12
Ex 3: Evaluate:
 (3  4) 2  3 12 


2
 8  3  2  11 
2
II
Simplifying Algebraic Expressions
The terms of an algebraic expression are those parts separated by addition (or
1
subtraction). The numerical part of the term is called its coefficient. The parts of each
term that are multiplied are called the factors of the term. One of the greatest challenges
to algebra students is remembering that factors are multiplied and terms are added or
subtracted. Like terms (those that have the same variable factors) can be added by
combining the coefficients. An algebraic expression is simplified when parenthese have
been removed and like terms have been combined.
Ex 4: Simplify:
3( x  3)  2(3x  1)  4(6  2 x)
Ex 5: Simplify:
18x  2 3x  2( x  3)  4
III
Translating as an algebraic expression
Ex 6: Write the English phrase as an algebraic expression. Then simplify. Let x
represent the number.
a)
A number increased by the difference between 5 and twice the number
b)
The product of 6 and the sum of a number, twice the number, and 2 .
IV
Mathematical models
We examined mathematical models in lesson 1 some. Remember, a mathematical model
is a formula to represent a real life situation.
Ex 7: Suppose the upper limit of range of a heart rate of an individual is given by
2
H  (220  a) in beats per minute where a is the age and the lower limit of range of a
3
2
heart rate of an individual is given by H  (220  a) .
5
a)
Find the upper and lower limit for someone aged 43.
2
b)
Suppose the actual upper limit for a 43 year old is 121 beats per minute.
Does the mathematical model overestimate or underestimate the actual heart rate
and by how much?
3